Fractal Geometry and Dynamics
September 4 - December 15, 2017
The mathematics of fractals has been enjoying an explosion of interest recently. Fractal geometry is a part of modern mathematical analysis. The fundamental research theme is to study and apply general geometric objects which are often so irregular that the methods of classical analysis are unsuitable or inefficient. Examples of such objects include various types of generalised surfaces, ranging from rectifiable sets to currents and varifolds, and fractal type sets and measures, for example, attractors of dynamical systems and related invariant measures.
The ever-widening interest in fractals has greatly invigorated other fields of mathematics, and on the other hand, other areas of mathematics have contributed to the enrichment of fractal geometry. Examples of the mutual enrichment include dynamics, mathematical physics, probability theory, calculus of variations, Fourier analysis, partial differential equations, complex analysis, number theory, and potential theory.
In recent years there has been a remarkable interaction between fractal geometry and dynamics. The field of modern dynamics emerged in the mid 1960’s, and since then, dynamical methods have proved to be extremely efficient in many fields of modern analysis. The program covers a variety of currently active research objectives and techniques to study open significant problems in fractal geometry – most of them closely related to dynamics. These include, for example, self-similar, self-affine and random structures, dimension theory as well as projection and slice theorems.